A closed vessel contains helium and ozone at a pressure of P atm.The ratio of He and Oxygen atoms is 1:1. If Helium is removed from the vessel,the pressure of the system will reduce to

To determine the new pressure of the system after removing helium from a closed vessel containing helium and ozone, we need to analyze the situation step by step. The initial conditions state that the ratio of helium (He) to ozone (O3) is 1:1, and the total pressure in the vessel is P atm.

Understanding the Initial Conditions

In the closed vessel, we have two gases: helium and ozone. Since the ratio of helium atoms to ozone molecules is 1:1, we can assume that for every mole of helium, there is one mole of ozone. This means that if we denote the number of moles of helium as n, we also have n moles of ozone.

Calculating the Initial Pressure

The total pressure in the vessel, P, is the sum of the partial pressures of the individual gases. According to Dalton's Law of Partial Pressures, the total pressure is given by:

• P_total = P_He + P_O3

Where P_He is the partial pressure of helium and P_O3 is the partial pressure of ozone. Since the ratio of the moles of helium to ozone is 1:1, we can express the partial pressures as:

• P_He = (n/2n) * P = (1/2)P
• P_O3 = (n/2n) * P = (1/2)P

Thus, the initial pressure of the system can be expressed as:

• P = P_He + P_O3 = (1/2)P + (1/2)P = P

Removing Helium from the System

When helium is removed from the vessel, we need to consider how this affects the total pressure. Since helium and ozone are the only gases present, removing helium will decrease the total number of moles of gas in the vessel.

New Pressure Calculation

After removing helium, we are left with only ozone in the vessel. The number of moles of ozone remains the same (n moles), but the moles of helium become zero. The new total number of moles in the vessel is now n moles of ozone.

Using the ideal gas law, we can express the new pressure (P_new) as:

• P_new = (n/V)RT

Since the volume (V) and temperature (T) remain constant, we can see that the pressure is directly proportional to the number of moles of gas. Initially, we had 2n moles (n of He and n of O3), and now we have only n moles (of O3). Therefore, the new pressure can be calculated as:

• P_new = (n/V)RT = (1/2)(P) = (1/2)P

Final Result

After removing helium from the closed vessel, the pressure of the system will reduce to:

• P_new = (1/2)P

This means that the pressure in the vessel is halved when helium is removed, leaving only the ozone gas contributing to the pressure. This scenario illustrates the principles of gas behavior and the impact of changing the number of gas moles in a closed system.